90 people are in a school.
14 of the females and
16 of the males wear glasses.
19 people wear glasses.
- How many females are there?
- How many males are there?
- How many people do not wear glasses?
|
Number |
Females |
Males |
Total |
90 |
4 u |
6 p |
Wear glasses |
19 |
1 u |
1 p |
No glasses |
|
3 u |
5 p |
(a)
Number of females = 4 u
Number of males = 6 p
4 u + 6 p = 90 --- (1)
1 u + 1 p = 19 --- (2)
(2)
x 4 4 u + 4 p = 76 --- (3)
(1) - (3)
(4 u + 6 p) - (4 u + 4 p) = 90 - 76
4 u + 6 p - 4 u - 4 p = 14
2 p = 14
1 p = 14 ÷ 2 = 7
Substitute 1 p = 7 into (2).
1 u + 1 p = 19
1 u + 7 = 19
1 u = 19 - 7 = 12
Number of females
= 4 u
= 4 x 12
= 48
(b)
Number of males
= 6 p
= 6 x 7
= 42
(c)
Number of females who do not wear glasses
= 4 u - 1 u
= 3 u
Number of males who do not wear glasses
= 6 p - 1 p
= 5 p
Number of people who do not wear glasses
= 90 - 19
= 71
Answer(s): (a) 48; (b) 42; (c) 71